Matrix Valued Truncated Toeplitz Operators

Abstract

This thesis contains results about the matrix valued truncated Toeplitz operators (MTTO's) de ned on the model space K = H2 H2(E), with a xed pure inner function and E an arbitrary Hilbert space. The class of MTTO's is denoted by T (K ). In the main work of this thesis we shall concern with the extension of some of the results obtained in the scalar case by D. Sarason in [27]. After gathering together the mathematical preliminaries of this work in Chapter 1, in Chapter 2 we shall present the most important properties of the model spaces K and some very important operators S and S in T (K ). The main object of this thesis is the study of the matrix generalization of the truncated Toeplitz operators introduced in [27]; a more recent presentation is [17]. This will be the content of Chapter 3, 4, 5. Finally, in Chapter 6 the preceding theory is applied to initiate the study of nite rank operators in T (K ).